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Time integration and discrete Hamiltonian systems

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Summary

This paper develops a formalism for the design of conserving time-integration schemes for Hamiltonian systems with symmetry. The main result is that, through the introduction of a discrete directional derivative, implicit second-order conserving schemes can be constructed for general systems which preserve the Hamiltonian along with a certain class of other first integrals arising from affine symmetries. Discrete Hamiltonian systems are introduced as formal abstractions of conserving schemes and are analyzed within the context of discrete dynamical systems; in particular, various symmetry and stability properties are investigated.

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Authors and Affiliations

  1. Division of Applied Mechanics, Department of Mechanical Engineering, Stanford University, 94305, Stanford, CA, USA

    O. Gonzalez

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  1. O. Gonzalez
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Additional information

Communicated by Stephen Wiggins and Jerrold Marsden

This paper is dedicated to the memory of Juan C. Simo

This paper was solicited by the editors to be part of a volume dedicated to the memory of Juan C. Simo.

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Gonzalez, O. Time integration and discrete Hamiltonian systems. J Nonlinear Sci 6, 449–467 (1996). https://doi.org/10.1007/BF02440162

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  • DOI: https://doi.org/10.1007/BF02440162

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